# Calculus volume stuff

posted by .

Find the volume of the solid obtained by rotating the region bounded
y = 16 x and y = 2 x^2 about y =0

Find the volume of the solid obtained by rotating the region bounded about the x-axis by y=4x^2, x =1, and y = 0

Find the volume of the solid generated by rotating the region bounded by
y = \sin^2(x) and y = 0
between 0 and pi about the x-axis

• Calculus volume stuff -

washers: v=∫[0,8] π(R^2-r^2) dx
where R=16x and r=2x^2
= 2621454/15 π

shells: v=∫[0,128] 2πrh dy
where r=y and h=√(y/2)-y/16
= 2621454/15 π

Can you set up the other integrals?

## Similar Questions

1. ### calculus edit

1. Find the volume formed by rotating the region enclosed by x=5y and x=y^3 with y is greater than or equal to 0 about the y-axis. 2. Find the volume of the solid obtained by rotating the region bounded by the given curves about the …
2. ### Calculus

This problem set is ridiculously hard. I know how to find the volume of a solid (integrate using the limits of integration), but these questions seem more advanced than usual. Please help and thanks in advance! 1. Find the volume of …
3. ### calculus

Consider the solid obtained by rotating the region bounded by the given curves about the line x = 4. x= 4y^2 , x = 4 Find the volume V of this solid.
4. ### CALCULUS 2

Consider the solid obtained by rotating the region bounded by the given curves about the line x = 1. y = x, y = 0, x = 4, x = 6 Find the volume V of this solid
5. ### calculus

Let A be the bounded region enclosed by the graphs of f(x) = x , g(x) = x3 . Find the volume of the solid obtained by rotating the region A about the line x + 2 = 0.
6. ### calculus

Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. y = 9 - 9x^2 , y = 0 Find the volume V of this solid. Sketch the region, the solid, and a typical disk or washer. Any help or tips would …
7. ### calculus

Sketch the region bounded by the curves y = x^2, y = x^4. 1) Find the area of the region enclosed by the two curves; 2) Find the volume of the solid obtained by rotating the above region about the x-axis; 3) Find the volume of the …
8. ### Calculus

a) Find the volume formed by rotating the region enclosed by x = 6y and y^3 = x with y greater than, equal to 0 about the y-axis. b) Find the volume of the solid obtained by rotating the region bounded by y = 4x^2, x = 1, and y = 0 …
9. ### CALCULUS MAJOR HELP!!!!!!

Find the volume of the solid obtained by rotating the region bounded y = 16 x and y = 2 x^2 about y =0 Find the volume of the solid obtained by rotating the region bounded about the x-axis by y=4x^2, x =1, and y = 0 Find the volume …
10. ### Calculus I don't understand

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = 10 x and y = 5 x^2 about y =0 Find the volume of the solid obtained by rotating the region bounded by y=8 x^2, x …

More Similar Questions